A Fully Nested 243×243 Unique-Prime Magic Square Constructed from Nine Disjoint 81×81 Prime Magic Blocks

A Fully Nested 243 x 243 Unique-Prime Magic Square Constructed from Nine Disjoint 81 x 81 Prime Magic Blocks This dataset contains a fully nested 243 x 243 magic square whose 59,049 entries are all globally distinct prime numbers. It extends the earlier 81 x 81 unique-prime magic-square construction by arranging nine mutually disjoint 81 x 81 prime magic-square blocks as a 3 x 3 macro-centre shell. This dataset presents a fully nested 243 x 243 magic square whose 59,049 entries are all globally distinct prime numbers. It extends the earlier 81 x 81 unique-prime magic-square construction by arranging nine mutually disjoint 81 x 81 prime magic-square blocks as a 3 x 3 macro-centre shell. The master centre is 10,000,000,033 and the global magic constant is 2,430,000,008,019 = 243 x 10,000,000,033. The square verifies at all aligned recursive levels: 6,561 aligned 3 x 3 blocks, 729 aligned 9 x 9 blocks, 81 aligned 27 x 27 blocks, 9 aligned 81 x 81 blocks, and the full 243 x 243 square, all computationally verified with zero failures. All entries are prime, globally unique, and congruent to 13 modulo 30. The verifier package includes a cleaned 243 x 243 CSV, exact verification reports, checksums, and a reproducible verification script. The cleaned CSV keeps exactly the first 243 rows and first 243 entries per row, removing spreadsheet/export artifacts from the source upload. The bundled verifier uses deterministic Miller-Rabin checks suitable for the dataset range. A separate SymPy software cross-check reproduced the same verification result. This is a verified finite computational construction. It does not claim an infinite family, a theorem about prime distribution, uniqueness of method, or optimality/minimality of the selected prime entries.